A detail from The Wonder Workshop, part of a retrospective at the Whitechapel .

Zebra finches flit about a dead apple tree, planted amid piles of books in a giant aviary at the Whitechapel Gallery. The birdschirp merrily, crapping on the books below. There are books everywhere: books on birds and novels with birds in their titles; books in the branches and underfoot. The branches are hung with pruning tools and pairs of binoculars – all the paraphernalia of the birdwatcher and of the hunter. “Aesthetics is to artists as ornithology is to birds,” the American painter Barnett Newman once quipped. The finches don’t care. They’ll crap on anything, even the portraits of David Attenborough and Alfred Hitchcock, nailed to the branches.

There is more to Mark Dion’s Theatre of the Natural World than birds, though they do show up everywhere. Dead mallard hang head down in a hunter’s corrugated iron hide, ready for the plucking. The interior is arranged for a meal. Fur and fowl decorate the crockery. Another hide is disguised as a giant hay bale, furnished with sofa and chairs, and decorated with antlers and a hunting horn. Another, looming above us like a forest watchtower, has camouflage-patterned walls and camo-covered furnishings. It is a wonder you can see it.

One upstairs gallery has been decked out as the naturalist’s study. Images of extinct animals decorate the rich, dark wallpaper. Among the naturalist’s bric-a-brac is a fake unicorn’s horn, an ammonite that turns out to be a carving of a snake and photos of polar bears in their icy habitat that are actually pictures of museum dioramas with stuffed animals. (Japanese photographer Hiroshi Sugimoto has done much better with his images of similar subjects).

Live birds near a picture of David Attenborough inside Dion’s Library for the Birds of London. Photograph: Guy Bell/Rex/Shutterstock

Dion’s own playful drawings are the highlight here – riffing on nature and human hubris. Later, I come across a drawing that shows the comparative size and weights of various animals – water buffalo (130lb, stag (275lb), komodo dragon (365lb). The artist Robert Smithson weighs in at 190lb.

All this is fun, though to my mind there is too much window-dressing and stage-setting, with desks, green-shaded library lights, fancy wainscoting. The cabinet of curiosities, real and fabricated, has been the subject of many exhibitions, as has the complex relationship between humans and other animals – though there is always more to be said.

In 2005, following a three-year residency at Manchester Museum and at the University of Manchester, Dion went through the museum archive to disinter a plethora of objects, from taxidermic specimens – a flock of birds in flight, a moth-eaten platypus, the head of a giant flatfish, mouth agape – to a crate filled with cockle shells and peculiar doctored photographs. Best of all is an old filing cabinet, whose hanging folders are labelled with a disturbing taxonomy: “Embalmed Ones”, “Stray Dogs”, “Suckling Pigs”, “Those That Are Trained”, “Mermaids”.

All this is fabulous – and what is not seen is more unnerving than what is displayed. These objects, images, files and other materials are housed in a fake office, filled with the accoutrements of some forgotten curator, who has become one with the objects of his research, holed-up in the bowels of a museum. This is a kind of Borgesian metafiction. Bureau of the Centre for the Study of Surrealism and Its Legacy, reads the sign on the glass door to this transplanted office.

The Bureau of the Centre for the Study of Surrealism and Its Legacy. Photograph: Whitechapel

In 1999, Dion and a group of volunteers mudlarked and beachcombed the Thames foreshore at low tide, at Millbank, in front of Tate Britain and at Bankside, in the shadow of the power station that would soon become Tate Modern. Pensioners, teenagers and even the occasional Tate curator joined in. The river police, staff from the Museum of London and ecologists offered help and advice. The final result – or perhaps the residue – is a huge cabinet, whose drawers, as fastidious as any lepidopterist’s, display bits of broken plates, the soles of shoes, oyster-shells, plastic bottle-tops, broken clay pipes, tide-washed and eroded toys.

The bulk of the cabinet is filled with plastic and cardboard boxes, neatly labelled. Mobile phones, cutlery, animal bones with butchery marks, cassette tapes, teeth, all have their box and their place. It is a land of lost dentures, phones hurled in lovelorn anger into the river, coins thrown for good luck, things stolen then abandoned, the wristwatches of the drowned – who knows what stories are here?

The final work, the Wonder Workshop, is a display of peculiar creatures, glowing with a green unearthly light in an otherwise darkened room, whose forms are derived from images in old engravings and books, some invented by their illustrators, others from actual objects. This is nature as the product of rumour, hearsay and misinterpretation. There are things that never lived, alongside spear-heads, medieval weaponry, coral trees, broken finials, and much besides. They fill the room – and my head – with an eerie bestiary.